fisica1-youn-e-freedman-exercicios-resolvidos

5.105: a) Newton’s 2nd law gives
dvy
mg
m = mg − kvy,
where = vt
dt
k
v y
∫
v
dv
y
− v
= −
k
m
∫
v y t
0 0
t
dt
This is the same expression used in the derivation of Eq. (5.10), except the lower limit
in the velocity integral is the initial speed v
0
instead of zero.
Evaluating the integrals and rearranging gives
v
= v e
0
−kt
m
+ v (1 − e
t
−kt
m
)
Note that at t = 0 this expression says v y
= v0
and at t → α it says v y
→ v t
.
b) The downward gravity force is larger than the upward fluid resistance force so the
acceleration is downward, until the fluid resistance force equals gravity when the
terminal speed is reached. The object speeds up until v y
= v . Take + y to be downward.
t
c) The upward resistance force is larger than the downward gravity force so the
acceleration is upward and the object slows down, until the fluid resistance force equals
gravity when the terminal speed is reached. Take + y to be downward.